Blog

Hello world!

longjidiscovery

longjidiscovery

[latexpage]
At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^*$:
\[
   f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
\]
where $h$ is some step.
Then we interpolate points $\{(x_k,f_k)\}$ by polynomial 
\begin{equation} \label{eq:poly}
   P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j}
\end{equation}
Its coefficients $\{a_j\}$ are found as a solution of system of linear equations:
\begin{equation} \label{eq:sys}
   \left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
\end{equation}
Here are references to existing equations: (\ref{eq:poly}), (\ref{eq:sys}).
Here is reference to non-existing equation (\ref{eq:unknown}).

Share this post

Share on facebook
Share on google
Share on twitter
Share on linkedin
Share on pinterest
Share on print
Share on email

This Post Has 7 Comments

  1. A WordPress Commenter

    16 Jun 2019 Reply

    Hi, this is a comment.
    To get started with moderating, editing, and deleting comments, please visit the Comments screen in the dashboard.
    Commenter avatars come from Gravatar.

  6. trusted_icEn

    4 Feb 2025 Reply

    Play only at trusted online casinos, for exciting wins.
    Choose reliable gaming sites, for guaranteed gambling pleasure.
    Guaranteed wins at the best online casinos, for maximum enjoyment and safety.
    Trust only trusted online casinos, for exciting wins in gambling.
    The best online casinos for every player, for thrilling gambling emotions.
    Play only at reliable online casinos, for exciting wins in gambling.
    Reliable online casinos for true gambling fans, for maximum enjoyment and safety.
    canadian online casino reviews http://www.royalspins-game.com/casino-reviews/canadian-casinos/ .

Leave a Reply

Close Menu